The scientific program of the Centre of Applied Mathematics (CAM) is based on the analysis of nonlinear differential equations and systems of differential equations modelling some types of stationary and nonstationary processes. Results and methods of functional analysis concerning the existence, multiplicity and stability of solutions of modelled nonlinear equations are deepened and further developed by CAM. Furthermore, the problems of bifurcations and stability are studied in the case of strongly nonlinear processes which can be described by variational inequalities, and general inclusions respectively, and which are motivated by biological and ecological models. Other analyzed questions concern systems of nonstationary nonlinear differential equations which contain some elliptic operator. They have not been answered satisfactorily yet and can be examined only partially by methods of numerical analysis.
It is necessary to create a team closely connected to the highly professional mathematical institute of the Academy of Science. Such a team should ensure the prospect of the scientific work in the field of nonlinear problems, as well as of studies of applied mathematics at the University of West Bohemia.
The scientific program of the Centre of Applied Mathematics can be divided into the following partial targets:
The partial targets stated above are connected by personalities of
Pavel Drabek and Milan Kucera, as well as by cooperation with some other
members of the Department of Mathematics (e.g. Alois Kufner, Stanislav
Mika, Petr Prikryl). This kind of cooperation is necessary since the numerical analysis requires a correct formulation of problems, including the basic information about the qualitative behaviour of the solutions. On the other hand, the theoretical research needs a reasonable stimulation provided by the numerical studies. The intention of the research group is to follow the scheme model - theory - numerical computation.
